There are a number of ways to look at defining responsibilities.
Smaller companies usually only require a single 'org chart'. I have seen some put it right in the front of their 'quality manual'.
Many companies have numerous organizational charts from high level 'corporate masters' down to the level of each individual department. In larger companies, it should be noted, that these are typically in a state of flux. New 'positions' are made and others are eliminated. It is important for you to note that these are Controlled documents. A somewhat common failure mode is a loss of control or not defining who is responsible for the control of the organizational charts.
I have shown you an example of an organizational chart. But remember, there are other ways in which companies define responsibilities. Bear this in mind because ISO and TS require you to defines responsibilities. My point is, look beyond an organizational chart.
A good example is your company's procedures. If we're talking level 2's, and you're using flow charts, you can put the functional position responsible by each step. CAUTION: Remember the concept of where some companies, especially large ones and 'tech' companies, tend to 'reorganize' on a somewhat regular basis. Ask yourself this: If a reorganization occurs, what will trigger someone to update the chart? On a high level, it may be a management review output. On a lower level it is often the case that the departmental manager is responsible for his or her departmental organizational chart. Never use specific names on an org chart unless you like to make a lot of changes or are a very stable, relatively small company.
So - we can look at procedures and, in many cases, even what many call work instructions, as vehicles to define responsibilities. In some cases inter-company memos define responsibilities. Many larger companies require departmental managers to notify specific people when they are not 'available' (vacation or whatever) and to specifically define who is assuming the manager's responsibilities while the manager is not available.